Geminal, definition

Geminal functional theory is a very promising research area. The different varieties of antisymmetrized products are very flexible and inherently handle difficult problems, like multideterminantal molecules. The computational effort is low compared to the quality of the solutions. The perturbation theoretical approach to SSG should essentially be possible for AGP and UAGP as well. The formal definition of GFT is a flexible framework that opens up many new opportunities for exploring the nature of solutions to the Schrodinger equation. 

Figure 1 A computational sequence of the CCSD-R12 geminal amplitude equation. For the definitions of symbols, see ref. 33.

Here an important definition for the rate constant of free carrier production, k, is given. The latter differs from the ionization rate constant by a multiplier equal to the charge separation quantum yield tpm, obtained in the Markovian approximation. This difference indicates that the number of photogenerated ions that avoid geminate recombination and become free is less than their total amount, cpm < 1. 

The geminate quantum yield of triplets is obtained by substitution of the corresponding kernels into definition (3.822) ... 

The geminal wave functions in eq. (2.60) in the SLG approximation are by definition obtained by diagonalizing the effective Hamiltonian for the m-th bond. These latter are as previously given by eq. (3.1) which can be recast to the form ... 

Chemistry of cyclopropane derivatives, which combine different sorts of activating substituents, has less definitely been investigated and their synthetic potentials have only recently been explored. Whereas geminally donor-acceptor-substituted systems 6 were treated in preceeding contributions to this series 5 6 7), this review will be confined to vicinally activated compounds 7. 

Figure 6. Definition of some silanol sites at steps (a) or at edges (b) between planes 111 of /3-cristobalite. The silicon atoms bonded to hydroxyl groups are shown by small dots. Only a few silanols are shown for sake of clarity. Full and open circles denote single and geminal hydroxyls, respectively.

Geminal alkylation (4,212-213). The definitive paper on geminal alkylation of ketones via cyclobutanones has been published. The original method involves dibromination of the cyclobutanone and consequently is not suitable for substrates containing isolated double bonds. In this case an alternative approach is available via a-trimethylenedithiocyclobutanones. Direct condensation of trimethylene dithiotosylate (4, 539-540 5, 71) with the cyclobutanone enolate fails, but can be accomplished indirectly by conversion of the cyclobutanone into an enamide by reaction with i-butoxybis(dimethylamino)-methane. The desired dithiane is then obtained by reaction of the enamide and trimethylenedithiotosylate in ethanol buffered with potassium acetate. The sequence is illustrated for 1-tetralone (1). The product (4) obtained in this way... 

It should be mentioned that the inverse (reverse ) anomeric effect has been postulated (183) recently for propanedinitrile CHjfCN) (95) and its derivatives, based on a synergistic destabilization by two geminal cyano substituents. The authors assumed that the anomeric effect always implies a stabilizing interaction between two substituents at an anomeric center (this assumption is not justified, see Section II.H) and a destabilizing interaction must therefore correspond to an inverse effect. However, such an assumption does not correspond to the definition of the anomeric (and reverse anomeric) effects, which is based on the relation between energies of conformers, not on the energy of interaction between substituents at an anomeric center. 

From the above definitions, the geminate polarization at t 0 is and the concentration of A - radicals. 

Our main focus here is on two typical situations arising in experimental studies of intermolecular ET in solutions. One is the bulk bimolecular reaction, where many particles are involved, and the other is the geminate reaction in an isolated donor-acceptor pair. For definiteness, we consider photoinduced ionization followed by geminate recombination that proceeds according to the scheme ... 

To calculate the orbital energies Sj corresponding to the CMOs 54 and the values of the coefficients a,b,c and d, one must first compute the necessary matrix elements. It follows from definitions 53 that the pseudo-2s orbitals (2s) do not form an orthogonal set (cf equations 55). If A are the self-energies and B the geminal crossterms... 

The T2 and T2 vector functions can be obtained in the way that is analogous to the case of the Ti residual. The function Eq. (129) is now projected onto the conventional doubles and geminal manifolds, Eqs. (131) and (132), where the following definition of the projection manifolds is used in the RHF formalism [5]... 

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